On Scattered Convex Geometries

Kira Adaricheva, Maurice Pouzet

Research output: Contribution to journalArticle

Abstract

A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice Ω(η), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalOrder
DOIs
Publication statusAccepted/In press - Nov 21 2016

Fingerprint

Convex Geometry
Geometry
Semilattice
Obstruction
Closure Space
Algebraic Lattice
Modular Lattice
Algebraic Geometry
Axiom
Closed set
Convex Sets

Keywords

  • Algebraic lattice
  • Convex geometry
  • Lattices of relatively convex sets
  • Lattices of suborders
  • Lattices of subsemilattices
  • Multi-chains
  • Order-scattered poset
  • Topologically scattered lattice

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

Adaricheva, K., & Pouzet, M. (Accepted/In press). On Scattered Convex Geometries. Order, 1-28. https://doi.org/10.1007/s11083-016-9413-0

On Scattered Convex Geometries. / Adaricheva, Kira; Pouzet, Maurice.

In: Order, 21.11.2016, p. 1-28.

Research output: Contribution to journalArticle

Adaricheva, Kira ; Pouzet, Maurice. / On Scattered Convex Geometries. In: Order. 2016 ; pp. 1-28.
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